[GAP Forum] GL( m, p ) x GL( n, p ) as a subgroup of GL( m+n, p )
Stefan Kohl
stefan at mcs.st-and.ac.uk
Wed Oct 28 11:41:23 GMT 2015
On Wed, October 28, 2015 10:22 am, Markus Szymik wrote:
>
> I would like to construct an isomorphic copy of the product GL( m, p ) x GL( n, p )
> as the subgroup of block matrices in GL( m+n, p ). What would you say is the
> best way to do it?
Ideally, there would already be a `DirectProduct' method which returns a group
in the desired representation. But since there is no such method so far, you can
use e.g. the following function:
DirectProductOfGLs := function ( m, n, p )
local G, gens_m, gens_n, gens_mn, g, h;
gens_m := GeneratorsOfGroup(GL(m,p));
gens_n := GeneratorsOfGroup(GL(n,p));
gens_mn := [];
for g in gens_m do
h := IdentityMat(m+n,GF(p));
h{[1..m]}{[1..m]} := g;
Add(gens_mn,h);
od;
for g in gens_n do
h := IdentityMat(m+n,GF(p));
h{[m+1..m+n]}{[m+1..m+n]} := g;
Add(gens_mn,h);
od;
G := Group(gens_mn);
return G;
end;
Hope this helps,
Stefan
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